2uData ⮞Regression & Correlation ⮞Overview of regression and correlation

Overview of regression and correlation

Consider two variables `X` and `Y` and their values `x` and `y`. These cases can occur:

• for each value `x_i` there is one value `y_i`,
• for each value `x_i` there are numerous values `y_(ij)`,
• for numerous values `x_(ij)` there is one value `y_j`,
• combination of previous cases.

To study the relationship between two numerical variables, we use frequently scatter plots. For each pair (`x_i`, `y_i`), there is a corresponding point in plot. Fig. 1 illustrates several main cases about relationship between two variables.

Fig. 1 Main cases about relationship between two numerical variables

Except Figure 7.1a, there are forms and degree of relationship between two numerical variables. In Figures 7.1b, 7.1c, 7.1d, 7.1e, the relationship can be presented by a line, this relationship is known as linear relationship. On the contrary, the relationship in Figure 7.1f is presented by a curve, this is nonlinear relationship.

Figure 7.1c represents a negative linear relationship, when `x` increases, its corresponding value `y` decreases. On the contrary, in Figure 7.1b, 7.1d, 7.1e, when `x` increases, its corresponding value `y` increases; this relationship is known as positive linearity.

When we proceeds from Figure 7.1b to 7.1e, the points become closer to straight line, the relationship becomes stronger.

Note

A strong relationship between two numerical variables does not assure that a causal relation exist between these variables. You can consult a funny discussion about this topic at the website of Tyler Vigen.